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Saturday, March 19, 2011

Hand Evaluation --Let me introduce you to the K & R‏

So someone tells you bridge is fun and you decide you want to learn to play. After all, you like playing cards in general. Your instructor sits down patiently and tells you that Aces are worth four points, Kings are worth three, etc. What he/she usually forgets to tell you, but what you find out later, is that this point count system is supposed to tell you the relative strength of the hand and help you in the bidding. So you learn to "open" hands with more than an average number of points in the deck per deal, usually 13 points.

As you evoke this rather simplistic hand evaluation technique, it becomes clear to you that this method is hopelessly inadequate. First off, barring a ruff, an A will take a trick, always. A king will only take a trick when the A is onside, i.e. half the time and risks getting ruffed. A "Q" is even more likely to become a nothing trick and if it's in rho's suit and lho hasn't raised, it's going to get ruffed out for sure. The proportions 4/3/2/1 just don't seem to be quite right. Thereby a hand such as this: AK,8732,A84,8742 and this: A874,7,87,AK8765 are given the same raw point count but the latter definitely has more trick-taking power. The raw point count technique definitely does not tell the whole story.

So if you're like most developing players, you're introduced to another evaluation strategy: the losing trick count. For most, losing trick count asks you to count one loser in each suit that is missing and A/K/Q. (Most experts make .5 loser adjustments for A vs Q but most "instructors" don't tell us that). Be that as it may, now hands like AK,8732,A84,8742 become eight loser hands and hands like A874,7,87,AK8765 become six loser hands and bidding decisions are made on these evaluations. This evaluation technique accounts for shape, but flattens out the honor cards A/K/Q and ignores J's completely to wit: A654,A65,A65,A65 and Q654,Q65,Q65,Q65 register the same 8 loser count (before the adjustments). Which hand would you rather have?

Thereby neither of the techniques above account for any card less than a J. Which hand would you rather have: AKT9,AT5,T93,K98 or this hand AK32,A32,432,K32? Would you rather have this six loser: A432,2,32,AK5432 or this six loser: AT98,T,T9,AKT9876? Or better yet this one: AJT9,J,JT,AKJ987.

Another example

This is "six" points (raw) but you can get four trick from it: KQJT9
This is "nine" points but only guarantees three tricks AKQ53

Luckily, we have very accomplished bridge players such as Kaplan/Rubens/Goldsmith who help us out of this dilemma. A very helpful tool for hand evaluation is the K & R hand evaluator applet:


I've used it tons as I learned the ins and outs of the trick-taking potential of my hands.

This hand evaluation tool adjusts the raw point count to something more realistic. The evaluator consistently correctly evaluates A/K's versus Q/J's. It accounts for shape as well. (incorporating losing trick count techniques). It adds the dimension of spot cards and adjusts if spot cards are present in long suits as opposed to short suits.

What is also remarkable about this tool is that it evaluates hands that might fit well opposite a possible hand partner may have. For example this hand: AKJT65,A65,A5,98 (K&R (AKJT76 A65 A5 98) = 20.00) is equal in strength to this hand AKQJT,A65,A54,98? (K&R (AKQJT A65 A54 98) = 20.00) Aren't both spade suits worth five tricks in general. Well "No!". Opposite Q, Q4,Q32,432,7432 hand number one will give you six tricks in the spade suit.

Here are some hands to help you test out the above theories. Figure out a raw point count, losing trick count and evaluator count. See what you get and see if the above phenom isn't presented in your outcome data. I can assure you it is!

Have fun.








Niels said...

I like your article and the subject very much, but I don't agree with your initial conclusion about the value of a K vs an A. For the K it is not just a question of the A being onside or offside, it may also be in partners hand, so the chances of getting a trick with the K is obviously better than the 50% you mentioned.

Isolde said...

You are correct Niels, if you hold a K and partner holds the corresponding ace, then it might take a trick if it doesn't get ruffed out. The K & R actually takes into account fitting cards opposite the hand being analyzed. Well done. However, an A doesn't need a K to back it up in order to take a trick --so if you compare odds based on whether one needs a back-up we're pretty much back to square one (or worse). I appreciated the discussion.